A bit was a unit of currency that existed in the form of a coin, which was used in California, United States of America on Earth during the late 19th century.
In 1893, after inadvertently traveling back in time, Lieutenant Commander Data asked a bellboy at the Hotel Brian for temporary lodging. The bellboy replied that it cost "six bits a day or four dollars a week."
The DVD subtitles on some region releases caption the sentence as "six pence a day, or four dollars a week.".
Later, when Data joined the local poker game, he was told that the ante was four bits. (TNG: "Time's Arrow")